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See detailShifting Martingale Measures and the Birth of a Bubble as a Submartingale
Föllmer, Hans UL; Biagini, Francesca; Nedelcu, Sorin

in Finance and Stochastics (2014), 18(2), 297-326

In an incomplete financial market model, we study a flow in the space of equivalent martingale measures and the corresponding shifting perception of the fundamental value of a given asset. This allows us ... [more ▼]

In an incomplete financial market model, we study a flow in the space of equivalent martingale measures and the corresponding shifting perception of the fundamental value of a given asset. This allows us to capture the birth of a perceived bubble and to describe it as an initial submartingale which then turns into a supermartingale before it falls back to its initial value zero. [less ▲]

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See detailRisk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles
Föllmer, Hans UL; Acciaio, Beatrice; Penner, Irina

in Finance and Stochastics (2012), 16(4), 669-709

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito et al. (Electron. J. Probab. 11(3):57–106, 2006). These risk measures ... [more ▼]

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito et al. (Electron. J. Probab. 11(3):57–106, 2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably penalised probability measures on the optional σ-field. This yields an explicit analysis both of model and discounting ambiguity. We focus on supermartingale criteria for time consistency. In particular, we show how “bubbles” may appear in the dynamic penalisation, and how they cause a breakdown of asymptotic safety of the risk assessment procedure. [less ▲]

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